Multilevel techniques in solving electromagnetic scattering problems

Summary form only given. Recently there has been renewed interest in solving integral equations due to the advent of fast multilevel techniques. These fast solvers exploit the special structure of the matrices that arise from the numerical approximation of the integral equation. The kernel of the integral equation is usually related to the Green´s function which is translationally invariant. This property manifests itself in the numerical approximations of the Green´s operator: the matrix has an inherent Toeplitz-like structure, or the matrix can be factored by translational matrices. As a result, an otherwise dense matrix vector multiplication can be performed in O(NlogN) operations. The authors review these methods.